Carroll and Downing's nightmare spell at Liverpool came to an end when West Ham splashed the cash to prize the outcasts to Upton Park before the start of the 2013/14 season.
The duo have been instrumental in West Ham's fight for survival, with Sam Allardyce's men now 11 points clear of the relegation zone after 32 rounds.
Sullivan reserved special praise for Carroll, who arrived in London for £15million - a club record fee.
Injuries have plagued Carroll's season but the England international striker has scored two goals in his last four games, including West Ham's opener in their 2-1 win over Sunderland on Monday, to play himself into contention for Roy Hodgson's FIFA World Cup squad.
"If Carroll had been fit all season, we'd have been pushing for Europe," Sullivan told Mirror Sport ahead of West Ham's clash with league-leading Liverpool at Upton Park on Sunday.
"We've averaged two points a game over the last nine games - and he’s still not match fit.
"I accept he didn't fit in with the style Liverpool play, but he's still a fantastic player and we're delighted with him.
"During the first half of the season, Andy was tremendously unlucky with injuries. But we at the club have always believed in him.
"He is an extremely motivated young man who still has his best years ahead of him and we're excited by that. I'm sure he'll be just as excited about coming up against his old club."
Sullivan added: "As for Stewart, he has had a fantastic season and has also been instrumental in helping us to climb to safety.
"Success is relative but these two players have helped us to stay in the Premier League and now we can continue to build."
